Renormalization from Density Functional Theory to Strong Coupling Models for the Electronic Structure of La 2 CuO 4
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RENORMALIZATION FROM DENSITY FUNCTIONAL THEORY TO STRONG COUPLING MODELS FOR THE ELECTRONIC STRUCTURE OF La 2 CuO 4 MARK S. HYBERTSEN*, MICHAEL SCHLUTER*, E.B. STECHEL** and D.R. ** JENNISON *AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974 "**Solid State Theory Division 1151, Sandia National Laboratories, Albuquerque, NM 87185
ABSTRACT Strong coupling models for the electronic structure of La2 CuO 4 are derived in two successive stages of renormalization. First, a three-band Hubbard model is derived using a constrained density functional approach. Second, exact diagonalization studies of finite clusters within the three band Hubbard model are used to select and map the low energy spectra onto effective one-band Hamiltonians. At each stage, some observables are calculated and found to be in quantitative agreement with experiment. The final results suggest the following models to be adequate descriptions of the low energy scale dynamics: (1) a spin 1/2Heisenberg model for the insulating case with nearest neighbor Jz 130 meV; (2) a "t--t '- J , model with nearly identical parameters for the electron and hole doped cases.
Proper treatment of the many-body correlations in the new Cu-O based superconductors is crucial to understanding their properties in the normal state as well as the mechanism for superconductivity. Several simplified models for the electronic structure of the Cu-O planes have been proposed which include strong interaction effects [1-6]. Previous work 11-4,6] emphasizes the phenomenology of a particular model as its parameters are varied rather than material-specific properties. Here we adopt the opposite approach. We start with an accurate quantum-chemical description of La2CuO 4 and proceed to renormalize down in energy to simplified few band models. We thus derive, from first principles, model parameters which explicitly reflect the properties of the materials and explicitly test the relevance of few (one) band models for the low energy dynamics. The local density functional approach (LDA) accurately predicts the cohesive properties of the Cu-O based materials 17]. The LDA energy bands also highlight the central role of the Cu-O pdor derived bands [8]. These findings strongly motivate the use of a three-band Hubbard model to describe low energy excitations in these materials: H ija•EJ•a~
2'Ji'l, H =EucQC.C-jCCJ,
Ki+C+ }, 7 CiiC- ,i+Ciu
(1)
where the ij indices label the planar Cu and 0 sites, and C'i creates holes with spin a 6 2 in Cu d(x 2 - y ) or 0 pa(x,y) orbitals relative to a Cu d1°, 0 p vacuum state. The undoped ground state corresponds to one hole per Cu0 2 unit. The one-electron parameters' (including on-site energy difference e=cP-ed and near-neighbor hopping t) and the Coulomb integrals (including on-site and near-neighbor U and near-neighbor exchange K) are illustrated in Fig. la. These parameters are effectively screened by all those (higher energy) degrees of freedom which have been explicitly discarded. Mat. Res. Soc. Symp. Proc. Vol. 169. '1990 Materials Res
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